In order to gain new insight in the ZnO system, we performed crystal structure prediction using simulated annealing with an empirical potential and local optimization on ab initio level, both at standard and elevated pressure. We have found the experimentally observed structure types [wurtzite (B4), sphalerite (B3), and rock salt (B1)] in agreement with previous research. In addition, many new interesting modifications were found in different regions of the energy landscape, such as the beta-BeO type, the GeP type, the NiAs type, and the so-called "5-5" type modification. At extreme conditions (>150 GPa), we observe a CsCl (B2) type of structure, and as a possible intermediate phase along the NaCl (B1) -> CsCl (B2) transition route, we suggest the alpha-WC (B-h) modification. Furthermore, we have investigated the electronic properties of ZnO structures. Our investigations offer new possibilities of tuning the band gap with pure zinc oxide by employing modifications with different structural arrangements.